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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Contiguity relations for generalized hypergeometric functions

Authors: Alan Adolphson and Bernard Dwork
Journal: Trans. Amer. Math. Soc. 347 (1995), 615-625
MSC: Primary 33C20; Secondary 33C80
MathSciNet review: 1283535
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Abstract: It is well known that the hypergeometric functions

$\displaystyle _2{F_1}(\alpha \pm 1,\beta ,\gamma ;t),{\quad _2}{F_1}(\alpha ,\beta \pm 1,\gamma ;t),{\quad _2}{F_1}(\alpha ,\beta ,\gamma \pm 1;t),$

which are contiguous to $ _2{F_1}(\alpha ,\beta ,\gamma ;t)$, can be expressed in terms of

$\displaystyle _2{F_1}(\alpha ,\beta ,\gamma ;t)\quad {\text{and}}{\quad _2}F_1^\prime (\alpha ,\beta ,\gamma ;t).$

We explain how to derive analogous formulas for generalized hypergeometric functions. Our main point is that such relations can be deduced from the geometry of the cone associated in a recent paper by B. Dwork and F. Loeser to a generalized hypergeometric series.

References [Enhancements On Off] (What's this?)

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  • [3] -, Hypergeometric functions and series as periods of exponential modules, Perspectives in Mathematics, Academic Press (to appear).
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Article copyright: © Copyright 1995 American Mathematical Society